Global stability of the steady states of an epidemic model incorporating intervention strategies
In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number $\mathcal{R}_0$ can be played an essentia...
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| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017056 |
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| author | Yongli Cai Yun Kang Weiming Wang |
| author_facet | Yongli Cai Yun Kang Weiming Wang |
| author_sort | Yongli Cai |
| collection | DOAJ |
| description | In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number $\mathcal{R}_0$ can be played an essential role in determining whether the disease will extinct or persist: if $\mathcal{R}_0 \lt 1$ , there is a unique disease-free equilibrium which is globally asymptotically stable; and if $\mathcal{R}_0 \gt 1$ , there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between $\mathcal{R}_0$ with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control. |
| format | Article |
| id | doaj-art-2570606e42bc4a25bd8bde31e8b4540e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2570606e42bc4a25bd8bde31e8b4540e2025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61071108910.3934/mbe.2017056Global stability of the steady states of an epidemic model incorporating intervention strategiesYongli Cai0Yun Kang1Weiming Wang2School of Mathematical Science, Huaiyin Normal University, Huaian 223300, ChinaSciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, USASchool of Mathematical Science, Huaiyin Normal University, Huaian 223300, ChinaIn this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number $\mathcal{R}_0$ can be played an essential role in determining whether the disease will extinct or persist: if $\mathcal{R}_0 \lt 1$ , there is a unique disease-free equilibrium which is globally asymptotically stable; and if $\mathcal{R}_0 \gt 1$ , there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between $\mathcal{R}_0$ with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.https://www.aimspress.com/article/doi/10.3934/mbe.2017056basic reproduction numberdisease-free equilibriumendemicspatial heterogeneity |
| spellingShingle | Yongli Cai Yun Kang Weiming Wang Global stability of the steady states of an epidemic model incorporating intervention strategies Mathematical Biosciences and Engineering basic reproduction number disease-free equilibrium endemic spatial heterogeneity |
| title | Global stability of the steady states of an epidemic model incorporating intervention strategies |
| title_full | Global stability of the steady states of an epidemic model incorporating intervention strategies |
| title_fullStr | Global stability of the steady states of an epidemic model incorporating intervention strategies |
| title_full_unstemmed | Global stability of the steady states of an epidemic model incorporating intervention strategies |
| title_short | Global stability of the steady states of an epidemic model incorporating intervention strategies |
| title_sort | global stability of the steady states of an epidemic model incorporating intervention strategies |
| topic | basic reproduction number disease-free equilibrium endemic spatial heterogeneity |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017056 |
| work_keys_str_mv | AT yonglicai globalstabilityofthesteadystatesofanepidemicmodelincorporatinginterventionstrategies AT yunkang globalstabilityofthesteadystatesofanepidemicmodelincorporatinginterventionstrategies AT weimingwang globalstabilityofthesteadystatesofanepidemicmodelincorporatinginterventionstrategies |